I am resident in CA, I was involved in car accident that took place on private property. I was waiting to make a left turn into a parking space after another vehicle had pulled out. After being a little more than a quarter ways into the parking space another vehicle hit me. My child was in the car and suffered injuries but I did not. I was hit so hard to the point where the impact slid me into the car that was parked to the left of me. I sustained damaged from right of bumper all the way down to the rear passenger door and on the left side from the bumper down to the end of driver side door. The other party only had damage to their front bumper, which actually came off. I spoke with both insurance companies and gave statements to my company and the other drivers company. I also sent photos of the accident before the cars were moved by the police to both the insurance companies. I just recently got two letters in the mail from the other party insurance company, one stating that their driver was not the proximate cause for my child injuries so they were denying the claim and the second stating that their driver was the proximate cause for the damage to my car and they were denying my claim. I don't understand by what they mean proximate cause.
I obtained a copy of the police report but it does not state who was at fault. The officer who responded to my 911 call indicated to me that that it would not be noted on the report because it took place on private property. The report does give the description of the accident as being a broadside and a explanation stating that V1 and V2 collided while the parties were trying to pull into the same parking stall. P1 and P2 both advised they had the right of way and were at the stall at the same time. The force of the impact forced V2 into the rear corner of V3.
The last correspondence I had from my insurance company was that they had made an appointment to view the surveillance video of the accident and would contact me so that I could attend with them, but nothing else since then.
I don't understand how the other party insurance could be denying liability, with the photos , police report and the option to view the video. In addition, how long does my insurance company have to determine liability?

They can deny liability because they don't want to pay. Just because they deny it doesn't mean a court of law will agree with them.

What you do at this point is ignore anything the other carrier says. Simply forward copies of any correspondence to the claims examiner of your carrier. Keep after the claims examiner to keep apprised of the status. Since the other carrier is denying the claim, your carrier will pay your damages, less any deductible and sue the other carrier on your behalf.

You might also want to consult a personal injury attorney. In cases like these most will work on a contingency basis.

It sounds like you were hit on the passenger side. This would mean you were making a left into the space while the other driver was making a right. So a claim could be made that you cut off the other driver. What I suspect happened was neither of you saw each other because of the car pulling out. So you both moved when the car vacating got out of the way. This would make fault a hard one to determine. I think the key will be how far you were into the space when you were hit.

Yes, proximate cause is basically who was the cause or who was at fault to make the accident happen. They are merely saying it is your fault, not their drivers fault. And is fairly common for many insurance companies to merely deny most claims before one side sues the other.

As noted, you merely turn it over to your company, let them pay you for the damages, and then allow them to sue the other party.

I agree with both ScottGem and Fr_Chuck - it is really easiest to let yor own insurance company handle the claim on your behalf. Initially they should pay for repairs to your car, minus the deductible amount you have for colllision coverage. If they are successful in being reimbursed by the other person's insurance company, they will refund you the deductible as well, and your insurance rates should not go up. One other bit of advice: talk to your insurance company to find out what repair shops they certify in your area - this way they can pay the repair shop directly, and you avoid any hassles of the shop saying you need somethig repaired and the insurace company denying it, or complaining that the costs are too high.